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871.
The scaling behavior of the molecular parameters of the hyperbranched polymers made by self-condensing vinyl polymerization 总被引:2,自引:0,他引:2
Ba XW Tian YL Diao JZ Wang SJ Wang HJ 《The European physical journal. E, Soft matter》2005,17(2):221-223
The hyperbranched polymers can be made by self-condensing vinyl polymerization without gelation transition. The average molecular weights, as well as the average sizes, can reach infinite values as the reaction is quantitatively completed, and the scaling forms of the molecular parameters should exist. In the paper, based on a recursion formula, the scaling form of the number fraction distribution and the number of the n-mers are given analytically as the conversion of double bonds is near 1. The mean square radius of gyration for very large hyperbranched polymers is calculated explicitly to give a scaling exponent. Finally, a scaling relation associated with the fractal dimension and the polydispersity exponent is given clearly. 相似文献
872.
Multibody systems including impacts with friction possess a rich dynamical structure, mainly due to their non-smooth and therefore
highly nonlinear characteristics together with the variety of multiple contact possibilities. Existing theories describe such
situations efficiently and correctly as has been proven by many practical applications. It can be shown, that even in large
multibody systems with many possible impacts very seldom two or more impacts occur at exactly the same time, usually impacts
are separated from each other. From this it makes sense to consider in more detail the structure of one impact alone and to
investigate the functional dependencies with respect to the initial magnitudes, namely normal and tangential relative velocities
and normal and tangential impulses before an impact. This paper describes the theory and gives examples. 相似文献
873.
Dan Butnariu 《Fuzzy Sets and Systems》1980,4(1):63-72
The aim of the paper is to explain new concepts of solutions for n-persons fuzzy games. Precisely, it contains new definitions for ‘core’ and ‘Shapley value’ in the case of the n-persons fuzzy games. The basic mathematical results contained in the paper are these which assert the consistency of the ‘core’ and of the ‘Shapley value’. It is proved that the core (defined in the paper) is consistent for any n-persons fuzzy game and that the Shapley values exists and it is unique for any fuzzy game with proportional values. 相似文献
874.
875.
Let {S
n}
n0 be a random walk on the line. We give criteria for the existence of a nonrandom sequence n
i for which
respectively
We thereby obtain conditions for to be a strong limit point of {S
n} or {S
n
/n}. The first of these properties is shown to be equivalent to
for some sequence a
i , where T(a) is the exit time from the interval [–a,a]. We also obtain a general equivalence between
and
for an increasing function fand suitable sequences n
i and a
i. These sorts of properties are of interest in sequential analysis. Known conditions for
and
(divergence through the whole sequence n) are also simplified. 相似文献
876.
Philippe Berthet 《Journal of Theoretical Probability》1997,10(3):557-579
We obtain outer rates of clustering in the functional laws of the iterated logarithm of Deheuvels and Mason(11) and Deheuvels,(7) which describe local oscillations of empirical processes. Considering increment sizes a
n 0 such that na
n and na
n(log n)–7/3 we show that the sets of properly rescaled increment functions cluster with probability one to the
n-enlarged Strassen ball in B(0, 1) endowed with the uniform topology, where
n 0 may be chosen so small as (log (1/a
n) + log log n)–2/3 for any sufficiently large . This speed of coverage is reduced for smaller a
n. 相似文献
877.
J. Nielsen Clelland 《Selecta Mathematica, New Series》1997,3(1):1-77
I consider the problem of computing the space of conservation laws for a second-order parabolic partial differential equation
for one function of three independent variables. The PDE is formulated as an exterior differential system on a 12-manifold M, and its conservation laws are identified with the vector space of closed 3-forms in the infinite prolongation of modulo the so-called "trivial" conservation laws. I use the tools of exterior differential systems and Cartan's method of
equivalence to study the structure of the space of conservation laws. My main result is: Theorem.
Any conservation law for a second-order parabolic PDE for one function of three independent variables can be represented by
a closed 3-form in the differential ideal
${\cal I}$
on the original 12-manifold M. I show that if a nontrivial conservation law exists, then has a deprolongation to an equivalent system on a 7-manifold N, and any conservation law for can be expressed as a closed 3-form on N that lies in . Furthermore, any such system in the real analytic category is locally equivalent to a system generated by a (parabolic)
equation of the formA (u
xx
u
yy
-u
2
xy
)+Bu
xx
+2Cu
xy
+Du
yy
+E = 0 where A, B, C, D, E are functions of x, y, t, u, u
x
, u
y
, u
t
. I compute the space of conservation laws for several examples, and I begin the process of analyzing the general case using
Cartan's method of equivalence. I show that the non-linearizable equation has an infinite-dimensional space of conservation laws. This stands in contrast to the two-variable case, for which Bryant
and Griffiths showed that any equation whose space of conservation laws has dimension 4 or more is locally equivalent to a
linear equation, i.e., is linearizable. 相似文献
878.
In this paper we are concerned with the problem of solving numerically isospectral flows. These flows are characterized by the differential equation
where is a symmetric matrix, is a skew-symmetric matrix function of and is the Lie bracket operator. We show that standard Runge-Kutta schemes fail in recovering the main qualitative feature of these flows, that is isospectrality, since they cannot recover arbitrary cubic conservation laws. This failure motivates us to introduce an alternative approach and establish a framework for generation of isospectral methods of arbitrarily high order.
879.
Atsushi Moriwaki 《Compositio Mathematica》1997,105(2):125-140
Let K be a function field and C a non-isotrivial curve of genus g2 overK. In this paper, we will show that if C has a global stable modelwith only geometrically irreducible fibers, then Bogomolov conjecture over function fields holds. 相似文献
880.
Agostino Prástaro 《Acta Appl Math》1998,51(3):243-302
Characterizations of quantum bordisms and integral bordisms in PDEs by means of subgroups of usual bordism groups are given. More precisely, it is proved that integral bordism groups can be expressed as extensions of quantum bordism groups and these last are extensions of subgroups of usual bordism groups. Furthermore, a complete cohomological characterization of integral bordism and quantum bordism is given. Applications to particular important classes of PDEs are considered. Finally, we give a complete characterization of integral and quantum singular bordisms by means of some suitable characteristic numbers. Some examples of interesting PDEs which arise in physics are also considered where existence of solutions with change of sectional topology (tunnel effect) is proved. As an application, we relate integral bordism to the spectral term
that represents the space of conservation laws for PDEs. This also gives a general method to associate in a natural way a Hopf algebra to any PDE. 相似文献